In spite of the myriad materials that have been fabricated and studied,
peculiar and intriguing solids continue to be discovered. In many of these
systems, the peculiarities are directly related to the spin magnetic moment,
or simply "spin", of the electron. One might think that this spin was put
on the electron primarily to amuse and occupy the materials physicist;
however, it vastly increases the number and variety of technological applications
of solid materials through the resulting magnetism. When an electron is
midway between being bound to one atom or being free to move among atoms,
novel behavior arises such as an extreme 'heaviness'. And complexity of
the material, such as requiring three, four, or five different elements
in a low symmetry arrangement adds to the richness of behavior. The understanding
and mathematical description of such complex materials is the focus of
my research.

Perhaps the most well known of such new materials are the high temperature
superconductors based on layers of copper and oxygen, where an 'up' spin
electron and a 'down' spin electron unite to form a bound superconducting
pair. New materials for thermoelectric applications have been grown based
on theoretical predictions on how to make the electrons more efficient
carriers of heat while making the vibrating atoms less efficient drains
of heat. Unusual magnetic materials in which the net 'up' spins and 'down'
spins are balanced on the whole but are unbalanced on the microscopic level
provide both new phenomena for study as well as the likelihood of new applications.
Such systems have been under study in my group. Examples of recent topics
follow.

Novel Magnetic Superconductors. Conventional superconductors
abhor magnetic fields. A superconductor sets up spontaneous electric currents
to shield it from applied magnetic fields, but a strong field ultimately
destroys the superconducting state. A new type of magnet, called a half-metallic
antiferromagnet, actually allows a novel type of superconductivity in which
only one type of spin, say up, becomes superconducting so up spins must
pair with up spins. Half-metallic ferromagnets are known; they have
inequivalent systems of up spin and down spin electrons, and one type is
metallic while the other is insulating (hence half-metallic). In
half-metallic antiferromagnets the up and down spins are balanced
on the whole. As a result, there is no intrinsic magnetic field as in a
ferromagnet, and the metallic electrons may pair to give a new type of
superconductor for which the current has a particular spin. If examples
of such "single spin superconductors" could be found, a wide variety of
completely new phenomena can be observed and studied theoretically.

There is one problem: there are no known half-metallic antiferromagnets.
We have been applying our computationally based theory of electronic behavior
and magnetism to attempt to predict materials that are good candidates
for this novel type of material. Compounds in the double perovskite structure
such as La2MnVO6 and La2CuVO6
appear to be candidates, but more searching, along with the involvement
of materials fabricators, is called for.

Exchange Interaction Constants for Magnetic Materials.
The sophisticated treatment of models dealing with the quantum mechanical
behavior of spins, by groups in our department as well as elsewhere, promises
to elucidate the underlying mechanism for novel magnetic behavior such
as in the exciting 'spin gap' and 'spin-Peierls' systems. The more interesting
compounds contain three or four important interaction constants, and it
is impossible to search the complete parameter space to find the constants
that provide the best explanation of the magnetic susceptibility or magnetic
resonance data. Our group has been calculating these exchange constants
using first principles methods. We find that their values are strongly
dependent on the particular atomic environment, which often is both low
symmetry and a combination of ionic and covalent bonded. Having the specific
values of the exchange constants allows physicists to focus their study
of spin systems to the regime of direct physical interest, which greatly
accelerates our understanding of complex materials systems. We expect to
extend this approach to combine first principles methods with the explicit
inclusion of many-body interactions.

Extending Theoretical Methods. The problem of describing the
behavior of electrons in condensed matter is a difficult one: the electrons
interact strongly and there is no natural small parameter to use in perturbation
theory. Density-functional based procedures rely on a self-consistent field
approach that gives excellent predictions unless inter-electronic correlations
become unusual (as it does for many of the systems discussed above). Our
group is strongly involved in formulating better approximations, implementing
them in numerical studies, and using them to interpret experimental data.